1. Technical Field
The invention relates to the field of Magnetic Resonance Imaging (MRI). In particular, the invention relates to a method, a computer program product and an apparatus which allow the correction of geometrical and intensity distortions inherent in Magnetic Resonance (MR) data.
2. Description of the Prior Art
MRI is a powerful technology for acquiring images with high tissue contrast. Besides the high tissue contrast, the potential for tumor localization and the possibility to scan in any plane orientation have made MRI a useful tool in many fields of medicine.
MRI relies on the principle that an arbitrary object of interest is magnetized by a strong and homogenous static magnetic field B0. The homogeneity of the static magnetic field B0 is a very important aspect of MRI because any perturbations of the homogeneity lead to geometry and intensity distortions in the image plane as well as to displacement, warp and tilt of the image plane itself.
In reality, the static magnetic field B0 is never homogeneous but perturbed. One reason for perturbations of the magnetic field B0 is the object of interest itself which is placed in the magnetic field B0.
When an object having a specific magnetic susceptibility distribution 102 (x) is placed in the homogeneous and static magnetic field B0, the object becomes magnetized and the homogenous static magnetic field B0 is distorted giving rise to an induced magnetic field B. For an analysis of the geometry and intensity distortions caused by an object placed in the homogeneous static magnetic field B0, the field B has to be determined.
In order to determine B, the Maxwell equations have to be solved. For a magnetostatic problem the Maxwell equations reduce to the Laplace equation
div(xcexcxcex94"PHgr"M)=0.xe2x80x83xe2x80x83(1)
Here "PHgr"M is the magnetic scalar potential in [Wb/m] and xcexc=1+"khgr"is the dimensionless magnetic permeability. If the susceptibility distribution 102 (x) of an object is known, "PHgr"M is determined by solving equation (1). From "PHgr"M the magnetic field H in [H/m]
H=xe2x88x92∇"PHgr"Mxe2x80x83xe2x80x83(2)
and the induced magnetic field B in [T]
B=xcexc0xcexc Hxe2x80x83xe2x80x83(3)
can be deduced. xcexc0 denotes the permeability of vacuum and has a value of xcexc0=4xcfx80xc3x9710xe2x88x927 H/m.
Equation (1) can be solved analytically for very simple objects such as cylinders and spheres. For more complex objects equation (1) can be solved only numerically. An exemplary numerical analysis of the magnetic field B for arbitrary magnetic susceptibility distributions "khgr"(x) in two and three dimensions is discussed in R. Bhagwandien: xe2x80x9cObject Induced Geometry and Intensity Distortions in Magnetic Resonance Imagingxe2x80x9d, PhD thesis, Universiteit Utrecht, Faculteit Geneeskunde, 1994, ISBN: 90-393-0783-0.
Susceptibility related distortions in MRI are usually in the millimeter range and have therefore no influence on diagnostic applications. However, in certain applications like Radio Therapy Planning (RTP) the geometric accuracy of an MR image is of high importance because accurate beam positioning is essential for optimal tumor coverage and sparing healthy tissues surrounding the tumor as much as possible.
Based on a numerical solution of equation (1), various methods have been proposed to reduce susceptibility induced distortions in MR images.
In the Bhagwandien document a correction method is described which is based on just one image, namely the distorted MR image. According to this correction method, the distorted MR image is first converted into a magnetic susceptibility distribution by segmenting the MR image into air and water equivalent tissue. In a next step the susceptibility distribution thus obtained is used to numerically calculate the field B. Finally, the corrected MR image is calculated on the basis of a read out gradient that is reversed with respect to the read out gradient used to acquire the distorted MR image. If for example a gradient field of a specific strength Gz has been applied during acquisition of the distorted MR image to define the image plane in z-direction, the corrected MR image is calculated for a gradient field of the strength-Gz.
A major draw back of all methods hitherto used to correct distortions in MR data is the computational complexity involved in generating corrected MR data. Consequently, there is a need for a method, a computer program product and an apparatus for correcting distortions in MR data faster.
This need is satisfied according to the invention by a method of correcting distortions in MR data, the method comprising the steps of providing distorted MR data of an object of interest and distortion parameters for one or more generic objects, determining transformation parameters correlating the object of interest and one or more of the generic objects, and processing the distorted MR data taking into account the distortion parameters and the transformation parameters to obtain corrected MR data.
By using generic distortion parameters, i.e. distortion parameters derived for generic objects, the corrected MR data for the object of interest can be generated faster. The reason for this is the fact that the Laplace equation (1) has not necessarily to be solved individually for every set of distorted MR data.
The distortion parameters for a particular generic object may be determined in various ways. The distortion parameters for a particular generic object may for example be derived from magnetic field inhomogenities which result from the specific magnetic susceptibility distribution of this particular generic object when the object is placed in a homogeneous static magnetic field. According to a first variant, the magnetic field inhomogenities caused by the generic object are determined by way of measurements. According to a second variant, the magnetic field inhomogenities are derived by way of calculations from distorted MR data of the generic object, i.e. from distorted generic MR data.
Preferably, the magnetic field inhomogenities, i.e. the distortion parameters, are derived from distorted generic MR data. Generic MR data may be obtained for e.g. a specific part of the human body from commercial databases. However, the generic MR data may also be generated using available generic objects during a data acquisition phase preceding the actual acquisition of the distorted MR data of the object of interest.
Deriving the magnetic field inhomogenities from generic MR data may include two separate steps. In a first step the magnetic susceptibility distribution of the generic object may be determined from the distorted generic MR data. To that end an image generated on the basis of the distorted generic MR data may be segmented automatically or manually to obtain areas of common or similar magnetic susceptibility. Then, an appropriate susceptibility value may be automatically or manually assigned to each area having the same or a similar magnetic susceptibility.
Once the magnetic susceptibility distribution of the generic object has been determined, the magnetic field inhomogenities are derived from the determined susceptibility distribution in a second step. The second step may include a numerical approach in order to solve the Laplace equation (1) for the determined susceptibility distribution. The numerical approach may for example be based oh transforming the Laplace equation (1) into a diffusion equation and on solving this diffusion equation by means of a diffusion technique. Preferably, however, a multi-grid approach is used to solve the Laplace equation (1) for the determined susceptibility distribution. By means of a multi-grid algorithm the computational complexity is reduced since the iterations that normally take place on a fine grid are replaced by iterations on a coarser grid.
The multi-grid approach is not restricted to solving the Laplace equation (1) in context with determining the distortion parameters for a generic object but can directly be applied to correct distortions in MR data xe2x80x9con-linexe2x80x9d. According to this xe2x80x9con-linexe2x80x9d aspect of the invention, the distorted MR data of the object of interest are first converted into a magnetic susceptibility distribution and the susceptibility distribution thus obtained is used to numerically calculate (using the multi-grid approach) the magnetic field B induced by the object of interest. The corrected MR data of this object may then be calculated on the basis of a read out gradient (i.e. gradient field strength) that is reversed with respect to the read out gradient used to acquire the distorted MR data of the object of interest.
In the course of correcting the distorted MR data of the object of interest a correlation between the object of interest and one or more of the generic objects has to be established. To this end transformation parameters indicative of the correlation are determined. The transformation parameters indicate how the object of interest will be deformed during a mapping operation on the one or more generic objects or how the one or more generic objects will be deformed during a mapping operation on the object of interest. Preferably, the transformation parameters are determined for specific points, contours, areas or other features which the object of interest and the one or more generic objects have in common.
The transformation parameters may be determined on the basis of magnetic susceptibility data of the object of interest and of the one or more generic objects. Preferably, the magnetic susceptibility data are derived from distorted MR data by e.g. segmenting the distorted MR data into regions of changing magnetic susceptibility (magnetic susceptibility contours) or regions (areas) of common or similar magnetic susceptibility. After the distorted MR data of the object of Interest have been segmented, transformation parameters are derived which deform at least one segmented region (e.g. a specific area or a specific contour) determined from the distorted MR data of the object of interest onto a corresponding region of one or more of the generic object or vice versa.
Once appropriate transformation parameters have been determined, the distorted MR data of the object of interest are corrected. To that end, the distortion parameters for the one or more generic objects and the transformation parameters may be used for calculating distortion parameters for the object of interest. Since the calculation of the distortion parameters for the object of interest involves a mere correlation of the distortion parameters for the one or more generic objects and the transformation parameters, no differential equation has to be solved. The distortion parameters for the object of interest can thus be obtained in a fast and easy manner. Once the distortion parameters for the object of interest are known, they may be reverse-applied to the distorted MR data of the object of interest or to data derived therefrom to obtain corrected MR data.
For a particular generic object several sets of distortion parameters may be provided for different gradient field strengths, different phase encoded directions, etc. This enables to select the set of distortion parameters that corresponds with respect to gradient field strength, phase encoded direction, etc. to the gradient field strength, phase encoded direction, etc. used while generating the distorted MR data of the object of interest.
MR data of a phantom object may be co-generated with the distorted MR data of the object of interest. By using a phantom object like a sphere or a cylinder with known characteristics it is possible to estimate the gradient field strength that was used while generating the distorted MR data of the object of Interest. As has been mentioned above, knowledge of the gradient field strength used while generating the distorted MR data of the object of interest is of importance e.g. if generic distortion parameters for different gradient field strengths are available.
Moreover, MR data of a phantom object co-generated with the distorted MR data of the object of interest allow to redundantly verify the correction of the distorted MR data. If for example the relationship between distorted and corrected MR data of the phantom object is known, this relationship may be compared to the relationship between the distorted and the corrected MR data of the object of interest. By comparing the two relationships a quality parameter for the corrected MR data of the object of interest can be derived.
Since the invention allows to correct geometry and intensity distortions in a fast and reliable manner, it is advantageous to repeatedly acquire and correct distorted MR data of the object of interest at different points in time. Due to the high reliability of the corrected MR data, chronological changes of the object of interest can be assessed. This enables for example to detect tumor growth in the sub-millimeter range. For this purpose MR data generated for one and the same object of interest at different points in time may be registered relative to each other. In the case of MR image data, the registration might result in a spatial superposition of the individual sets of MR image data.
According to a preferred aspect of the invention the corrected MR data of the object of interest are combined with Computer Tomography (CT) or fluoroscopic data of the object of interest to profit from the individual advantages of each imaging technology. For example the CT or fluoroscopic data and the corrected MR data of the object of interest may be registered relative to each other and the registered data may be used for generating an image showing a combination of the structures of the object of interest that were detected by MR on the one hand and by e.g. CT on the other hand.
Preferably, the corrected MR data or data derived therefrom like CT or fluoroscopic data registered with the corrected MR data are used for generating a graphical display for example on a display device of a computer system. The corrected MR data or the data derived therefrom may then be used for navigating a chirurgical tool or a pointer during e.g. bone surgery. To that end, an infrastructure may be provided which allows to determine on-line the current position of at least one of the surgical tool and the pointer with respect to the corrected MR data or the data derived therefrom. By superimposing the current position of at least one of the surgical tool and the pointer on the graphical display of the corrected MR data or the data derived therefrom a navigation aid for the surgical tool or the pointer is achieved. In the context of navigating a surgical tool or a pointer the fact that geometry and intensity distortions in the MR data of the object of interest have been corrected is of high importance because otherwise an exact navigation would not be possible.
The method according to the invention can be implemented as a hardware solution and as a computer program product comprising program code portions for performing the individual steps of the method when the computer program product is run on a computer. The computer program product may be stored on a computer readable recording medium like a data carrier attached to or removable from the computer.
The hardware solution includes an apparatus comprising a common database or separate databases for at least temporarily storing distorted MR data of the object of interest and distortion parameters determined for one or more generic objects, a transformation parameter generator for generating transformation parameters correlating the object of interest and one or more of the generic objects, and a generator for corrected MR data for processing the distorted MR data taking into account the distortion parameters and the transformation parameters to obtain corrected MR data for the object of interest. Preferably, the apparatus is part of a navigational infrastructure for computer aided surgery.